Me im on a timer

dante is leading a parade across the main street in front of city hall. starting at city hall, he marches the parade 4 blocks east, then 3 blocks south. from there, the parade marches 1 block west and 9 blocks north and finally stops. what is the vector displacement and direction of the the parade, starting from the city hall and the stopping point?

displacement: 6.71 m, direction: 63.4 degrees north of east displacement: 8.01 m, direction: 21.9 degrees north of east displacement: 2.56 m, direction: 39.7 degrees north of east displacement: 4.31 m, direction: 88.1 degrees north of east

Displacement: 6.71 m, Direction: 63.4 degrees north of east

Explanation:

In the attached image we can aprecciate each one of the movements of the parade. Let's say that the parade started from the origin (point (0,0)) then it moves to the east 4 blocks it means now the parade is located at point (4,0).

Then the parade went to the south three blocks, so it moves to the coordinate (4,-3). After this the parade went to the west one block so the new coordinate point is (3, -3).

And finally the movement of the 0 parade was 9 blocks to the north. It means the final point is now (0,9) - (3,-3) = (3,6)

And the displacement will be defined by the folliwing vector operation:

We know that the magnitude of the displacement vector is defined by the phytagoras theorem

And the angle will be defined by:

tan(beta)=3/6

beta = tan^-1(6/3)

beta = 63.43°

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west